After completing his sports studies Elizondo began his refereeing in 1992 in the Argentine Primera División. His international debut, he played on October 9, 1994 at the international match between Ecuador and Colombia. Since then, the physical education teacher worked among other things as Impartial in the Copa Libertadores 2002 and 2005, the Copa América in 1997 and 1999 and the 2004 Summer Olympics.
He belonged to Refereeaufgebot at the Football World Cup 2006 in Germany and introduced alongside the opening game Germany - Costa Rica on June 9 in Munich, the games against the Czech Republic Ghana, South Korea against Switzerland and the quarter-final match between England and Portugal.
On 9 July 2006, he also launched the final between Italy and France and was the first referee, who was put up for the opening and final match of World Cup. He is the first Argentine who was employed as a referee in a World Cup Final. In the extension of the game, he showed the Frenchman Zinedine Zidane after a head butt against Marco Materazzi the red card; this was the first sending-off, which was pronounced in the extension of a World Cup final. The red card is up to now often discussed as Elizondo has not even seen the assault and sent off only after the Note of the fourth official Luis Medina Cantalejo Zidane. Shortly after the World Cup 2006, he announced his retirement as a referee.